We study the isolated singularities of functions satisfying (E) (−∆) s v±|v| p−1 v = 0 in Ω\{0}, v = 0 in R N \Ω, where 0 < s < 1, p > 1 and Ω is a bounded domain containing the origin. We use the Caffarelli-Silvestre extension to R + × R N. We emphasize the obtention of a priori estimates, analyse the set of self-similar solutions via energy methods to characterize the singularities.